Question

A chain of mass m and length/lies on a horizontal table. The chain is allowed to slide down gently from the side of the table. Find the speed of the chain at the instant when last link of the chain slides from the table. Neglect friction everywhere.

• A. $\sqrt{gl}$
• B. $\sqrt{2gl}$
• C. $\sqrt{3gl}$
• D. $\sqrt{5gl}$

Answer 1

The correct option is A $\sqrt{gl}$

The distance of center of mass of the chain from the corner of the table when the chain just slides off the table=$\frac{l}{2}$.

Thus Change in gravitational potential energy=$mg\frac{l}{2}$

This change goes into the gain in kinetic energy of the chain=$\frac{1}{2}m{v}^2$

$⟹mg\frac{l}{2}=\frac{1}{2}m{v}^2$

$⟹v=\sqrt{gl}$